Problem: A circle has a sector with area $1\pi$ and central angle $10^\circ$. What is the area of the circle? ${36\pi}$ $\color{#9D38BD}{10^\circ}$ ${1\pi}$
The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{10^\circ}{360^\circ} = 1\pi \div A_c$ $\dfrac{1}{36} = 1\pi \div A_c$ $A_c \times \dfrac{1}{36} = 1\pi$ $A_c = 1\pi \times 36$ $A_c = 36\pi$